Reproducing JPM’s US Rates Strategy RV Trade Idea¶

Note - Treasuries: The first cut is the deepest (20 September 2024)¶

91:100 3.125% Nov-41/ 2% Nov-41 flattener¶

Turning to relative value, we’ve noticed that originally issued 20-year bonds maturing in late-2041 and early-2042 have cheapened relative to our par curve, whereas originally issued 30-year bonds with similar maturities have outperformed. Clearly, the recent steepening of the Treasury curve supports wider yield spreads between higher-coupon OI 30s, and lower-coupon OI 20s with the same maturity, given significant duration differences. However, this dynamic is not explained by duration profiles: Figure 20 displays the securities in the 2040–2043 basket, sorted by modified duration and shows that late-41/ early-42 OI 30s appear rich relative to other securities with similar duration. In particular, the 3.125% Nov-41/ 2% Nov-41 curve appears 5.0bp too steep relative to the shape of the 15s/20s Treasury par curve (Figure 21). Hence, we recommend initiating 91:100 weighted 3.125% Nov-41/ 2% Nov-41 flatteners (see Trade recommendations).

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In [13]:
import sys

sys.path.append("../../")
In [14]:
from CurveInterpolator import GeneralCurveInterpolator
from CurveDataFetcher import CurveDataFetcher
from utils.rv_utils import cusip_spread_rv_regression
from utils.viz import plot_usts
from models.calibrate import calibrate_mles_ols, calibrate_nss_ols
from models.NelsonSiegelSvensson import NelsonSiegelSvenssonCurve
In [15]:
import pandas as pd
import numpy as np
import scipy
from datetime import datetime
from typing import Dict, List
import tqdm

import matplotlib.pyplot as plt
import matplotlib.pylab as pylab
params = {
    "axes.titlesize": "x-large",
    "legend.fontsize": "x-large",
    "axes.labelsize": "x-large",
    "xtick.labelsize": "x-large",
    "ytick.labelsize": "x-large",
}
pylab.rcParams.update(params)

import seaborn as sns
sns.set(style="whitegrid", palette="dark")

import nest_asyncio
nest_asyncio.apply()

import warnings
warnings.filterwarnings('ignore', category=FutureWarning)
warnings.filterwarnings('ignore', category=pd.errors.SettingWithCopyWarning)
warnings.filterwarnings('ignore', category=RuntimeWarning)

import plotly
plotly.offline.init_notebook_mode()

%load_ext autoreload
%autoreload 2

The autoreload extension is already loaded. To reload it, use:
  %reload_ext autoreload
In [16]:
curve_data_fetcher = CurveDataFetcher(use_ust_issue_date=True)
In [17]:
quote_type = "eod"
as_of_date = datetime(2024, 9, 20)

curve_set_df = curve_data_fetcher.build_curve_set(
    as_of_date=as_of_date,
    sorted=True,
    include_off_the_run_number=True,
    market_cols_to_return=[f"{quote_type}_price", f"{quote_type}_yield"],
    calc_free_float=True,
    use_github=True,
)

curve_set_df
Out[17]:
cusip security_type auction_date issue_date maturity_date time_to_maturity int_rate high_investment_rate is_on_the_run ust_label ... parValue percentOutstanding est_outstanding_amt corpus_cusip outstanding_amt portion_unstripped_amt portion_stripped_amt reconstituted_amt free_float rank
0 912797LJ4 Bill 2024-08-22 2024-08-27 2024-09-24 0.010959 NaN 5.335 False 5.335% Sep-24 ... 7.426366e+08 0.003085 2.407091e+11 NaN 0.000000e+00 NaN 0.000000e+00 NaN -742.6366 16.0
1 912797LK1 Bill 2024-08-29 2024-09-03 2024-10-01 0.030137 NaN 5.263 False 5.263% Oct-24 ... 7.639260e+08 0.003311 2.307445e+11 NaN 0.000000e+00 NaN 0.000000e+00 NaN -763.9260 15.0
2 912797LS4 Bill 2024-09-05 2024-09-10 2024-10-08 0.049315 NaN 5.171 False 5.171% Oct-24 ... 7.725101e+08 0.003348 2.307550e+11 NaN 0.000000e+00 NaN 0.000000e+00 NaN -772.5101 14.0
3 912797LT2 Bill 2024-09-12 2024-09-17 2024-10-15 0.068493 NaN 5.053 True 5.053% Oct-24 ... 7.980483e+08 0.003458 2.307985e+11 NaN 0.000000e+00 NaN 0.000000e+00 NaN -798.0483 13.0
4 912797LU9 Bill 2024-08-22 2024-08-27 2024-10-22 0.087671 NaN 5.238 False 5.238% Oct-24 ... 4.965473e+08 0.003300 1.504905e+11 NaN 0.000000e+00 NaN 0.000000e+00 NaN -496.5473 12.0
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
388 912810TT5 Bond 2023-10-12 2023-10-16 2053-08-15 28.920548 4.125 NaN False 4.125% Aug-53 ... 8.606596e+09 0.120247 7.157430e+10 912803GU1 7.157430e+10 60954881.0 1.061942e+10 991450.0 52348.2848 4.0
389 912810TV0 Bond 2024-01-11 2024-01-16 2053-11-15 29.172603 4.750 NaN False 4.750% Nov-53 ... 4.567153e+08 0.006874 6.644364e+10 912803GW7 6.644364e+10 56812091.9 9.631553e+09 1679110.0 56355.3766 3.0
390 912810TX6 Bond 2024-04-11 2024-04-15 2054-02-15 29.424658 4.250 NaN False 4.250% Feb-54 ... 2.211754e+09 0.031064 7.119879e+10 912803GY3 7.119879e+10 58204025.7 1.299477e+10 792000.0 55992.2712 2.0
391 912810UA4 Bond 2024-07-11 2024-07-15 2054-05-15 29.668493 4.625 NaN False 4.625% May-54 ... 7.428279e+09 0.097202 7.642080e+10 912803HB2 7.642080e+10 68393441.8 8.027362e+09 1220467.0 60965.1628 1.0
392 912810UC0 Bond 2024-09-12 2024-09-16 2054-08-15 29.920548 4.250 NaN True 4.250% Aug-54 ... 4.964611e+09 0.095537 5.196507e+10 912803HD8 2.975507e+10 29061214.1 6.938548e+08 15000.0 24096.6028 0.0

393 rows × 25 columns

Build Par Curve Model¶

In [18]:
def liquidity_premium_curve_set_filter(curve_set_df: pd.DataFrame):

    # remove OTRs, olds, double olds, triple olds
    curve_set_filtered_df = curve_set_df[
        (curve_set_df["rank"] != 0) & (curve_set_df["rank"] != 1) & (curve_set_df["rank"] != 2) & (curve_set_df["rank"] != 3)
    ]

    # remove TBills
    curve_set_filtered_df = curve_set_filtered_df[curve_set_filtered_df["security_type"] != "Bill"]

    # remove low free float bonds (< $5bn)
    curve_set_filtered_df = curve_set_filtered_df[curve_set_filtered_df["free_float"] > 5000]

    # filter out bonds very close to maturity
    curve_set_filtered_df = curve_set_filtered_df[curve_set_filtered_df["time_to_maturity"] > 30 / 360]

    # remove CTDs
    curve_set_filtered_df = curve_set_filtered_df[
        ~curve_set_filtered_df["cusip"].isin(
            [
                curve_data_fetcher.ust_data_fetcher.cme_ust_label_to_cusip("4.625s 2026-09-15")["cusip"],  # TU
                curve_data_fetcher.ust_data_fetcher.cme_ust_label_to_cusip("4.125s 2027-09-30")["cusip"],  # Z3N
                curve_data_fetcher.ust_data_fetcher.cme_ust_label_to_cusip("4.25s 2029-02-28")["cusip"],  # FV
                curve_data_fetcher.ust_data_fetcher.cme_ust_label_to_cusip("4.25s 2031-06-30")["cusip"],  # TY
                curve_data_fetcher.ust_data_fetcher.cme_ust_label_to_cusip("4.375s 2034-05-15")["cusip"],  # TN
                curve_data_fetcher.ust_data_fetcher.cme_ust_label_to_cusip("4.625s 2040-02-15")["cusip"],  # US
                curve_data_fetcher.ust_data_fetcher.cme_ust_label_to_cusip("4.5s 2044-02-15")["cusip"],  # TWE
                curve_data_fetcher.ust_data_fetcher.cme_ust_label_to_cusip("4.75s 2053-11-15")["cusip"],  # UL
            ]
        )
    ]

    curve_set_filtered_df = curve_set_filtered_df.sort_values(by=["time_to_maturity"])

    return curve_set_filtered_df


def no_filter(curve_set_df: pd.DataFrame):
    return curve_set_df
In [19]:
# filter and fit bspline w/ knots are liquidity points
curve_set_filtered_df = liquidity_premium_curve_set_filter(curve_set_df=curve_set_df)

filtered_fitted_interpolator = GeneralCurveInterpolator(
    x=curve_set_filtered_df["time_to_maturity"].to_numpy(),
    y=curve_set_filtered_df[f"{quote_type}_yield"].to_numpy(),
)

fitted_bspline = filtered_fitted_interpolator.b_spline_with_knots_interpolation(
    knots=[0.5, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 15, 20, 25],
    k=3,
    return_func=True,
)

nss_func, status_nss, _ = calibrate_nss_ols(
    curve_set_filtered_df["time_to_maturity"].to_numpy(),
    curve_set_filtered_df[f"{quote_type}_yield"].to_numpy(),
)
assert status_nss

mles_func, status_mles = calibrate_mles_ols(
    curve_set_filtered_df["time_to_maturity"].to_numpy(),
    curve_set_filtered_df[f"{quote_type}_yield"].to_numpy(),
    overnight_rate=5.31,
    N=9,
)
In [20]:
plot_usts(
    curve_set_df=curve_set_df,
    ttm_col="time_to_maturity",
    ytm_col=f"{quote_type}_yield",
    hover_data=[
        "issue_date",
        "maturity_date",
        "cusip",
        "original_security_term",
        "ust_label",
        f"{quote_type}_price",
        "free_float",
    ],
    ust_labels_highlighter=[
        ("3.125% Nov-41", "red"), ("2.000% Nov-41", "blue"), 
    ],
    zero_curves=[(fitted_bspline, "BSpline k=3 - Zero Filtered Fit"), (nss_func, "Nelson Siegel Svensson"), (mles_func, "Merrill Lynch Exponential Spline")],
    par_curves=[(fitted_bspline, "BSpline k=3 - Par FF",)],
    impl_spot_n_yr_fwd_curves=[(fitted_bspline, 1, "Impl Spots, 1y Fwd")],
    impl_par_n_yr_fwd_curves=[(fitted_bspline, 1, "Impl Par, 1y Fwd")],
    title=f"All USTs - using {f"{quote_type}_yield"} - as of {as_of_date}"
)
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Fetching historical curve sets to regress 3.125% Nov-41/ 2% Nov-41 flattener vs our fitted model over time¶

In [21]:
start_date = datetime(2024, 3, 1)
end_date = datetime(2024, 9, 20)

curve_sets_dict_df, fitted_curves_dict = curve_data_fetcher.fetch_historical_curve_sets(
    start_date=start_date,
    end_date=end_date,
    fetch_soma_holdings=True,
    fetch_stripping_data=True,
    calc_free_float=True,
    fitted_curves=[
        ("LPF", f"{quote_type}_yield", liquidity_premium_curve_set_filter),
        ("NSS", f"{quote_type}_yield", no_filter, calibrate_nss_ols),
    ],
)

FETCHING CURVE SETS...: 100%|██████████| 181/181 [00:02<00:00, 68.62it/s]
AGGREGATING CURVE SET DFs: 100%|██████████| 181/181 [00:07<00:00, 22.82it/s]

Better data structure to fetch specific CUSIP timeseries data¶

  • Comparing different curve building methods on different filtering strats
In [22]:
cusip_timeseries: Dict[str, List[Dict[str, str | float | int]]] = {}
fitted_cubic_spline_timeseries: Dict[datetime, scipy.interpolate] = {}
fitted_bspline_timeseries: Dict[datetime, scipy.interpolate] = {}
fitted_smooth_spline_timeseries: Dict[datetime, scipy.interpolate] = {}
nss_timeseries: Dict[datetime, NelsonSiegelSvenssonCurve] = {}

for dt in tqdm.tqdm(curve_sets_dict_df.keys(), desc="Main Loop"):
    fitted_cubic_spline = fitted_curves_dict[dt]["LPF"].b_spline_with_knots_interpolation(
        knots=[0.5, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 15, 20, 25],
        k=3,
        return_func=True,
    )
    fitted_bspline = fitted_curves_dict[dt]["LPF"].b_spline_with_knots_interpolation(
        knots=[0.5, 1, 2, 3, 4, 5, 7, 8, 9, 10, 15, 20, 25], k=5, return_func=True
    )
    fitted_smooth_spline = fitted_curves_dict[dt]["LPF"].b_spline_with_knots_interpolation(
        knots=[0.5, 1, 2, 3, 5, 7, 10, 20], k=4, return_func=True
    )
    curr_nss_model = fitted_curves_dict[dt]["NSS"]

    fitted_cubic_spline_timeseries[dt] = fitted_cubic_spline
    fitted_bspline_timeseries[dt] = fitted_bspline
    fitted_smooth_spline_timeseries[dt] = fitted_smooth_spline 
    nss_timeseries[dt] = curr_nss_model

    curr_curve_set_df = curve_sets_dict_df[dt]
    curr_curve_set_df["lpf_cubic_spline_spread"] = curr_curve_set_df["eod_yield"] - fitted_cubic_spline(curr_curve_set_df["time_to_maturity"])
    curr_curve_set_df["lpf_bspline_spread"] = curr_curve_set_df["eod_yield"] - fitted_bspline(curr_curve_set_df["time_to_maturity"])
    curr_curve_set_df["lpf_smooth_spline_spread"] = curr_curve_set_df["eod_yield"] - fitted_smooth_spline(curr_curve_set_df["time_to_maturity"])
    curr_curve_set_df["nf_nss_spread"] = curr_curve_set_df.apply(
        lambda row: row["eod_yield"] - curr_nss_model(row["time_to_maturity"])
        if pd.notna(row["eod_yield"]) and curr_nss_model(row["time_to_maturity"]) is not None
        else np.nan, axis=1
    )

    for _, row in curr_curve_set_df.iterrows():
        if row["cusip"] not in cusip_timeseries:
            cusip_timeseries[row["cusip"]] = []

        payload = {
            "Date": dt,
            "cusip": row["cusip"],
            f"{quote_type}_yield": row[f"{quote_type}_yield"],
            f"{quote_type}_price": row[f"{quote_type}_price"],
            "lpf_cubic_spline_spread": row["lpf_cubic_spline_spread"],
            "lpf_bspline_spread": row["lpf_bspline_spread"],
            "lpf_smooth_spline_spread": row["lpf_smooth_spline_spread"],
            "nf_nss_spread": row["nf_nss_spread"],
            "free_float": row["free_float"],
            "est_outstanding_amount": row["est_outstanding_amt"],
            "soma_holdings": row["parValue"],
            "soma_holdings_percent_outstanding": row["percentOutstanding"],
            "stripped_amount": row["portion_stripped_amt"],
            "reconstituted_amount": row["reconstituted_amt"],
            "lpf_cubic_spline": fitted_cubic_spline,
            "lpf_bspline": fitted_bspline,
            "lpf_smooth_spline": fitted_smooth_spline,
            "nf_nss": curr_nss_model,
        }
        
        cusip_timeseries[row["cusip"]].append(payload)

Main Loop: 100%|██████████| 142/142 [00:04<00:00, 31.47it/s]
In [25]:
label1 = "3.125% Nov-41" 
label2 = "2.000% Nov-41" 

cusip_spread_rv_regression(
    curve_data_fetcher=curve_data_fetcher,
    label1=label1,
    label2=label2,
    cusip_timeseries=cusip_timeseries,
    fitted_splines_timeseries_dict={
        "lpf_cubic_spline": fitted_cubic_spline_timeseries,
        "lpf_bspline": fitted_bspline_timeseries,
        "lpf_smooth_spline": fitted_smooth_spline_timeseries,
        "lpf_smooth_spline": fitted_smooth_spline_timeseries,
    },
    benchmark_tenor_1=15,
    benchmark_tenor_2=20,
)
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lpf_cubic_spline is Benchmark Spline
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                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     3.125% Nov-41 / 2.000% Nov-41   R-squared:                       0.697
Model:                                       OLS   Adj. R-squared:                  0.695
Method:                            Least Squares   F-statistic:                     321.6
Date:                           Sun, 06 Oct 2024   Prob (F-statistic):           4.30e-38
Time:                                   19:01:56   Log-Likelihood:                 415.41
No. Observations:                            142   AIC:                            -826.8
Df Residuals:                                140   BIC:                            -820.9
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
===========================================================================================
                              coef    std err          t      P>|t|      [0.025      0.975]
-------------------------------------------------------------------------------------------
const                      -0.0968      0.008    -12.434      0.000      -0.112      -0.081
lpf_cubic_spline_15s20s     0.6568      0.037     17.934      0.000       0.584       0.729
==============================================================================
Omnibus:                       26.082   Durbin-Watson:                   0.256
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               43.882
Skew:                           0.881   Prob(JB):                     2.96e-10
Kurtosis:                       5.076   Cond. No.                         34.9
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
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Using lpf_cubic_spline for UST Metrics Calcs

3.125% Nov-41 Metrics Calc: 142it [00:03, 36.90it/s]
2.000% Nov-41 Metrics Calc: 142it [00:03, 38.00it/s]
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